The Effect of Sample Size on Mean & Median

Sample size is an important consideration in an experiment's design. A sample size that is too small will skew the results of an experiment; data collected may be invalid due to the small number of people or objects tested. Sample size has an effect on two important statistics: the mean and the median.

Sample Size and Experimental Design

Most experiments are run by comparing how two groups of people or objects react to a variable. Everything other than the variable is kept the same in order to avoid confusion when interpreting results. The number of people or objects in each group is known as the sample size. The sample size must be large enough to defeat the possibility that results occur due to random chance factors rather than to the manipulated variable. For example, a study of how being read to at night affects children's ability to learn to read would not be valid if only five children were studied.

Mean and Median

After the experiment is over, scientists use statistics to help them interpret the results of the experiment. Two important statistics are the mean and the median.

The mean, the average value, is calculated by adding all the results for a group and dividing by the number of people in the group. For example, if the average test score on a reading test for a group of children was 94 percent, this means that the scientist added all the test scores together and divided by the number of students, yielding an answer of approximately 94 percent.

The median refers to the number separating the higher half of the data from the lower half. It is found by arranging the data in numerical order. For example, the median score of all students taking a reading test could be 83 percent if half the students scored higher than 83 percent and half the students scored lower.

Mean and Sample Size

If the sample size is too small, the mean scores will be artificially inflated or deflated. Suppose only five students took a reading test. An average score of 94 percent would require most of those students to have scored near 94 percent. If 500 students took the same test, the mean could reflect a wider variety of scores.

Median and Sample Size

Similarly, the median scores will be unduly influenced by a small sample size. If only five students took a test, a median score of 83 percent would mean that two students scored higher than 83 percent and two students scored lower. If 500 students took the test, the median score would reflect the fact that 249 students scored higher than the median score.

Sample Size and Statistical Significance

Small sample sizes are problematic because the results of experiments involving them are not usually statistically significant. Statistical significance is a measurement of how likely it is that results occurred by random chance. With small sample sizes, it is generally extremely likely that results were due to random chance rather than to the experiment.